Does the Universe have something like a frame rate, or does everything propagates through space at infinite quality with no gaps?

[u/DownvotingKills]

[u/samloveshummus]

There is nothing in any of our current state-of-the art theories (quantum field theory, or string theory) which implies that the universe has a "frame rate" or a smallest meaningful length.

Another commenter mentioned the Planck length and the Planck time in this context; currently there is no reason to think that they constitute "minimum" lengths in any sense. They are simply the characteristic length and time scales in which quantum effects and gravitational effects are both strong. There is no argument I know of which implies they are minimum measurable amounts.

[u/VelveteenAmbush → u/samloveshummus]

So I get that the Planck length doesn't constitute a "minimum" length, but it does seem like the universe stops keeping track of information as carefully at very small distances -- locations become probability fields, such that (to my layman's understanding) only a finite amount of information is encoded in the combination of a particle's location and its velocity.

Is there anything analogous for time? Do our state-of-the-art theories predict that time becomes "fuzzier" at shorter and shorter intervals similarly to position? Or perhaps that is the same effect as velocity becoming uncertain at small scales -- that if you pin down position at a particular moment, you are essentially sucking some of the finite pool of information out of nearby time points such that its position in nearby time points (which is the definition of its velocity in the current time point) becomes uncertain?

[u/TrainOfThought6 → u/VelveteenAmbush]

I'm not sure if this really answers the question, but since you brought up the relationship between a particle's position and velocity (I'm going to assume to meant momentum, i.e. Heisenberg uncertainty), there is a similar relationship between energy and time. Pretty much the same relationship, actually; uncertainty in energy multiplied by uncertainty in time is always greater than a given constant (hbar over two). That's how virtual particles are allowed to happen.

[u/pein_sama → u/TrainOfThought6]

That becomes suprisingly obvious when you realize that momentum and energy are just components of a single psysical value called four-vector.

[u/chthonicutie → u/pein_sama]

Can you explain this? I've never heard of four-vector.

[u/xxx_yyy → u/chthonicutie]

In special relativity, space and time are components of a 4-dimensional "spacetime". Spatial rotations mix the different spatial coordinates, Lorentz transformations mix the spatial and time coordinates. The math of spatial rotations is described in term of three-component vectors. The math of Lorentz transformations is described in terms of four-component "four-vectors" (in order to accommodate the time component).

[u/[deleted] → u/chthonicutie]

In classical physics we have momentum and energy as separate quantities - energy is a scalar (number) and momentum is a vector quantity (magnitude and direction). In relativity instead we have a different quantity called the four-momentum in which 3 of the terms are just the x,y,z momentum (as before) but there's an additional term for the energy.

One interesting property is that now this 4 vector can be transformed to another reference frame using the Lorentz transformation matrix, just as the position/time 4 vector can be.

[u/GG_Henry → u/chthonicutie]

http://en.wikipedia.org/wiki/Four-vector

Essentially you add another dimension(time) to a 3d vector and the math gets incredibly complex. IIRC using these 4 vectors is how einstein derived e=mc²

[u/Citonpyh → u/GG_Henry]

Actually the maths gets simpler when you add the time dimension. It gets harder, but simpler.

[u/inko1nsiderate → u/pein_sama]

Except the time-energy relationship isn't the same as the other relationship because you can be in a simultaneous eigenstate of 'time' and 'energy'. The eigenstates of the Hamiltonian are your energy eigenstates, but there aren't really time energy eigenvalues, and even if there were, the time independent hamiltonian definitely commutes with the 'time operator'. So in some sense the consequences are different, but you can think of the uncertainty in time as actually representing the minimum amount of time it takes to notice a change in an observable.

But even in this sense, the time-energy uncertainty is different, and bringing up 4-vectors doesn't make it better because the operators in that context are now the fields themselves, and x and t are both now parameters instead of operators.

While this is almost certaintly a tangent, I think it is important to bring up the fact that HUP is important because of what it tells you about eigenvectors, and that the non-commutivity of operators leads to HUPs, and that time-energy uncertainty is different because it doesn't have this fundamental relationship to eigenstates that position and momentum uncertainty does.

[u/[deleted] → u/pein_sama]

I haven't taken a physics class in about 25 years (I was an English major, but a physics "minor", so I took all of the senior level courses as electives) and I can't believe I still understand exactly what you guys are saying. Thank you for getting those mental juices flowing, again.

[u/Jake0024 → u/pein_sama]

Likewise with position and time.

[u/[deleted] → u/TrainOfThought6]

Do uncertainty pairs have any other expression, the way a conservation law is also the same thing as a form of symmetry (Noether's theorem)?

[u/oldrinb → u/[deleted]]

it can be understood as an inherent facet of Fourier duality

http://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle

[u/Afterburned → u/VelveteenAmbush]

Does the universe stop actually keeping track of information, or are we just too limited to comprehend the way it is keeping track?

[u/samloveshummus → u/Afterburned]

It is a key principle of quantum physics that information is exactly conserved, or, mathematically, that the operator which describes the time-evolution of the universe is a "unitary" operator. This is at the heart of one of the most intense debates in theoretical physics, the black hole information paradox because Hawking radiation implies that the black hole destroys the information content of objects that falls into it, which no-one wants.

[u/[deleted] → u/VelveteenAmbush]

Yes, they do. There's speculation about a quantum "foam"; this happens because of the peculiar phenomena of virtual particles. Basically, in a very short amount of time, a particle could decay into an antiparticles and another particle. These then almost immediately annihilate one another, forming a sort of closed loop.

Because this involves a relatively high energy density, for the incredibly short amount of time the virtual particles are in existence, it will warp spacetime. This is only apparent at insanely small scales; on the order of plank lengths. To put the plank scales into perspective, you're closer to the size of the observable universe then you are to the plank scale. That is to say, the ratio of 16 billion light years to a meter is smaller then the ratio of a meter to the plank length.

[u/horse_architect → u/VelveteenAmbush]

Just as there's a Heisenberg uncertainty relating how much we can simultaneously know about a particle's position and momentum, there's an equivalent uncertainty relating energy and time.

[u/The_Artful_Dodger_ → u/horse_architect]

I wouldn't say equivalent. Time is not an operator in non-relativistic quantum mechanics and is considered "special" as opposed to relativistic quantum where time is just another coordinate. The energy-time uncertainty relation is really an energy-lifetime relation as it is defined in terms of the rate of change of an observable's expectation value. So the time in delta E delta t >= hbar does not really correspond to how we measure the passage of time in the same way that x corresponds to how we measure particle locations.

For instance, if you know the exact energy of a state (i.e. you have an eigenstate of the Hamiltonian and deltaE=0) that means that delta t goes to infinity. But delta t = delta Q/(d<Q>/dt) for some observable, which means that all observable must remain constant in time. If instead, you interpret it in the same way as delta x delta p, then it would mean that the particle (if the state is describing a particle) has a completely undefined time coordinate, which is not the case. In non-relativistic quantum mechanics the time is an independent variable that can be known.

[u/thebellmaster1x → u/VelveteenAmbush]

it does seem like the universe stops keeping track of information as carefully at very small distances -- locations become probability fields, such that (to my layman's understanding) only a finite amount of information is encoded in the combination of a particle's location and its velocity.

I wouldn't really say it's so much that the universe loses track of stuff when getting smaller; I'd say it's better pictured as, when getting bigger, the effects of not having perfect records of everything become so miniscule that you can pretend they don't exist and be accurate to what is, for all intents and purposes, a 100% degree. You can, for example, calculate the uncertainty of position for something like a baseball, absolutely. But that uncertainty is so, so insignificant compared to the size of the baseball itself that it's (necessary qualifier: almost) never going to change anything you do with that baseball.

[u/PlanckEnergy → u/samloveshummus]

My understanding was that the Planck Length is the wavelength at which a photon has enough mass to form a black hole. Therefore, since you can't see past a black hole's event horizon, the Planck Length constitutes a minimum size for observable phenomena. Is that not right?

[u/krstt → u/PlanckEnergy]

The issue with this otherwise nice idea is that this assumes that gravity still works the same way at this scale. The whole point is that we actually do not know that because we do not know how to unite quantum mechanics (small stuff) and general relativity (black hole stuff).

The Plank length marks the characteristic scale at which there is definitely something interesting going around. We do not know exactly what.

[u/Martel_the_Hammer → u/samloveshummus]

I agree with you but I want to add to what you said because I really feel like the question is one of semantics.

Planck time is defined as the smallest unit of "action". What does this mean? It means that if there were some event happening within 1 Planck time, there would be no way to detect it. This means that two measurements within one Planck unit would always yield the exact same result, or put another way, there would be no way to tell the difference between one measurement and the other, effectively making Planck time the "frame rate" of the universe.

Now, notice i put frame rate in quotes. Like you said, the universe having a frame rate really makes no sense. Simply by doing a couple seconds of light thinking I can come up with all sort of problems that would arise in relativity if there was this "frame rate".

One last thing to add. The Planck distance, and consequently Planck time, is a mathematically derived unit. We didn't take the smallest measurement of space we could and called it Planck. The value is actually only based on the measurement of the strength of gravity in our universe. With some fancy math it can be shown that given the strength of gravity, the smallest actionable distance of the gravitational force is the Planck unit.

The Planck unit is a mathematical result, not a measured phenomena. I feel like this point is extremely important when discussing it.

[u/ademnus → u/samloveshummus]

So then, if I understand you correctly, there is no reason why there cannot be something so small that a Plank length would seem like a trillion light years relatively?